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Inference by Eye: Confidence Intervals and How to Read Pictures of Data.
Abstract
Wider use in psychology of confidence intervals (CIs), especially as error bars in figures, is a desirable development. However, psychologists seldom use CIs and may not understand them well. The authors discuss the interpretation of figures with error bars and analyze the relationship between CIs and statistical significance testing. They propose 7 rules of eye to guide the inferential use of figures with error bars. These include general principles: Seek bars that relate directly to effects of interest, be sensitive to experimental design, and interpret the intervals. They also include guidelines for inferential interpretation of the overlap of CIs on independent group means. Wider use of interval estimation in psychology has the potential to improve research communication substantially.
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“Difference score CIs that did not overlap with zero would indicate that the two estimates were significantly different from one another (Cumming & Finch, 2005; Knezevic, 2008), even though the absolute or unstandardized contribution of A remained constant.”
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“05) roughly corresponds with an overlap in confidence intervals of one quarter of the length of the intervals, or half one arm of the interval, given sufficient sample size and no large differences in width (Belia et al. 2005; Cumming and Finch 2005).”
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“Cumming and Finch (2005) noted that when SEMs are relatively similar in magnitude, two independent means differ at the p .05 level of significance when they are separated by about 3 or more SEMs and they differ at the p .01 level when they are separated by about 4 or more SEMs.”
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“With both of these types of paired data, inferences should be made based on the mean paired difference and the CI of this mean difference (Cumming and Finch, 2005).”
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“A 95% confidence interval (CI) for an ROC area that excluded .50 was considered statistically significant predictive accuracy ( Cumming & Finch, 2005).”
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“Therefore, we calculated the 95 % confidence interval for each sample mean value, and non-overlap of confidence intervals between two means can be taken as a measure that the means are significantly different (Cumming and Finch 2005).”
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“The upper and lower bound estimates denote the range of plausible values for alpha should a scale be distributed to another sample drawn from the same population as the original sample (Cumming & Finch, 2005).”
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Liong, M., & Cheng, G. H. ‐. (2018) · The Journal of Sex Research · doi:10.1080/00224499.2018.1438576 · Cited by 35
“In addition, some of the associations found were accompanied by a rather wide confidence interval, suggesting that they are qualified by certain factors (Andrade, 2015; Cumming & Finch, 2005).”
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Peña-Araya, V., Pietriga, E., & Bezerianos, A. (2019) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2019.2934807 · Cited by 35
de Andrade, A. C. (2019) · Ecology and Evolution · doi:10.1002/ece3.5518 · Cited by 35
“To compare density between areas with different levels of ur‐ banization, I examined the degree of overlap between confidence interval (Cumming & Finch, 2005).”
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“However, we urge caution in interpreting statistical significance on the basis of these error bars alone, since two values can still be statistically significantly different despite having overlapping error bars (Cumming and Finch 2005).”
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“However, the confidence interval overlap indicated that the experience mediation path was significantly smaller than the agency mediation path (see Cumming and Finch, 2005).”
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“differences between groups despite overlapping error bars in the various figures (Cumming and Finch, 2005).”
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“It does, however, affect the ability to use ‘‘inference by eye’’ [10, 11].”
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“The degree to which the end-to-end of the error-bars touch or moderately overlap shows the significant differences between the groups (cf. Cumming & Finch, 2005).”
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“While it is often recommended that instead of comparing intervals of two (potentially dependent) samples it is better to compare intervals of the difference [75], nevertheless these types of multiple interval visualizations are commonly seen in scientific publications.”
BackgroundRees, M. W., Pascoe, J., Le, M., Robley, A. J., Birnbaum, E. K., Wintle, B. A., & Hradsky, B. A. (2023) · Journal of Applied Ecology · doi:10.1111/1365-2664.14402 · Cited by 33
Adil, M. S. (2014) · Global Journal of Flexible Systems Management · doi:10.1007/s40171-014-0084-7 · Cited by 33
“…addition, there are a number of authors (e.g.,Harlow et al. 1997; Johnson 1999; Thompson 1999; Krueger 2001; Gliner et al. 2002; Schmidt and Hunter 2002; Cumming and Finch 2005; Levine et al. 2008) who have further detailed the problems with null hypothesis significance testing (henceforth, NHST).”
BackgroundHoi, C. K. W., Zhou, M., Teo, T. P., & Nie, Y. (2017) · Psychology in the Schools · doi:10.1002/pits.22025 · Cited by 42
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“A 95% confidence interval contains the true mean 95% of the time and conveys effect sizes [17], making it possible to estimate differences.”
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Bergquist, P., Marlon, J., Goldberg, M. H., Gustafson, A., Rosenthal, S., & Leiserowitz, A. (2022) · Thinking & Reasoning · doi:10.1080/13546783.2022.2030407 · Cited by 27
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“Following Cumming and Finch (2005), we plot CIs instead of SE bars.”
MethodTestosterone and year‐round territoriality in tropical and non‐tropical songbirds
Goymann, W., & Landys, M. M. (2011) · Journal of Avian Biology · doi:10.1111/j.1600-048x.2011.05464.x · Cited by 33
Translating the impact of exercise on cognition: Methodological issues in animal research
Hatchard, T., Ting, J., & Messier, C. (2014) · Behavioural Brain Research · doi:10.1016/j.bbr.2014.06.043 · Cited by 33
Wright, A. G. C., Hallquist, M. N., Swartz, H. A., Frank, E., & Cyranowski, J. M. (2013) · Journal of Consulting and Clinical Psychology · doi:10.1037/a0034430 · Cited by 32
“The 95% CIs provide the researcher with model parameter precision estimates necessary for making statistical inferences (but see Cumming & Finch, 2005, for a detailed discussion on interpreting overlapping CIs by eye).”
Bleske-Rechek, A. L., Remiker, M. W., & Baker, J. P. (2009) · Individual Differences Research · doi:10.65030/idr.07014 · Cited by 33
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Herrmann, L., Barkmann, C., Bindt, C., Fahrenkrug, S., Breu, F., Grebe, J., & Becker-Hébly, I. (2023) · Archives of Sexual Behavior · doi:10.1007/s10508-023-02674-8 · Cited by 36
“If confidence intervals overlap, the results do not significantly differ from each other (Cumming & Finch, 2005).”
ResultAlmeida, G. J., Irrgang, J. J., Fitzgerald, G. K., Jakicic, J. M., & Piva, S. R. (2016) · Physical Therapy · doi:10.2522/ptj.20150407 · Cited by 33
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Young, J., Young, J. L., & Shaker, Z. (2012) · TechTrends · doi:10.1007/s11528-012-0600-6 · Cited by 32
“Cummings and Finch (2005) suggest that Confidence intervals have four major advantages.”
Confidence Intervals Make a Difference
Hoekstra, R., Johnson, A. M., & Kiers, H. (2012) · Educational and Psychological Measurement · doi:10.1177/0013164412450297 · Cited by 15
“Confidence intervals (CIs) are frequently mentioned as an alternative for NHST (e.g., Cumming & Finch, 2005; Kline, 2004; Schmidt & Hunter, 1997).”
BackgroundMethodResultInfluentialDhinaut, J., Chogne, M., & Moret, Y. (2017) · Developmental & Comparative Immunology · doi:10.1016/j.dci.2017.10.017 · Cited by 32
“Differences between each female treatment at each time point after oviposition (or egg age) were highlighted by estimating the degree of overlap of the 95% confidence intervals (CI), following recommendations by Cumming and Finch (2005).”
MethodBoedeker, P. (2020) · Scholarworks (University of Massachusetts Amherst) · doi:10.7275/5vvy-8613 · Cited by 32
Severe wildfires promoted by climate change negatively impact forest amphibian metacommunities
Beranek, C. T., Hamer, A. J., Mahony, S. V., Stauber, A., Ryan, S. A., Gould, J. A., Wallace, S., Stock, S. E., Kelly, O. W., Parkin, T., et al. (2023) · Diversity and Distributions · doi:10.1111/ddi.13700 · Cited by 32
“The importance of estimates for individual covariates was determined by 95% CIs that did not overlap with zero, although a slight overlap of the CI with zero was still assumed to confer statistical importance (Cumming & Finch, 2005).”
BackgroundEfficacy of self-control and patience interventions in adolescents
Schnitker, S. A., Felke, T. J., Fernandez, N. A., Redmond, N. M., & Blews, A. E. (2016) · Applied Developmental Science · doi:10.1080/10888691.2016.1178578 · Cited by 33
“8Error bars are not displayed on the graphs due to recommendations from Cummings and Finch (2005) concerning the display of within-subjects change.”
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Simons, M., & Kursawe, A.-L. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00264 · Cited by 32
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Matthews, W. J. (2011) · Judgment and Decision Making · doi:10.1017/s1930297500004265 · Cited by 31
“There has been a growing emphasis on reporting effects sizes and their associated confidence intervals (CIs, see, e.g., Cumming & Finch, 2005 ).”
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“We report actual p values for all coefficients in order to “move from NHST [null hypothesis significance testing] as dichotomous decision making to the consideration of p values as useful input to interpretation” (Cumming & Finch, 2005, p. 172).”
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“As the nature of our data does not allow us to directly assess the significance of the differences between point estimates (since both predictor variables are not measured on the same day), we followed an inference technique by Cumming and Finch (2005) to make these comparisons.”
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“In all models, odds ratios were determined to be significantly larger than others if their 95% confidence intervals did not overlap (Cumming and Finch, 2005).”
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“To judge the direction and magnitude of effects, we use CIs, rather than p values (e.g., Gelman and Tuerlinckx, 2000; Cumming and Finch, 2005).”
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“Unlike cases where an arm-specific mean is being compared with constant, pairwise comparisons of means based on the overlap method involve uncertainty in the centers of both CIs under inspection [41].”
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“, effect sizes with bootstrapped [12] confidence intervals [13] (see Figure 6).”
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“These approaches tend to offer more effective ways to compare and integrate findings from precedent and replication studies (Cumming & Finch, 2005; Gelman & Stern, 2006; Hubbard, 2016).”
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“Statistical reformers seek to reduce reliance on NHST and p values (Cohen, 1990, 1994; Thompson, 1996), primarily through the use of CIs (Harlow, Mulaik, & Steiger, 1997), which have the advantage of providing information about precision and statistical significance (Cumming & Finch, 2001, 2005).”
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“Conventional confidence intervals represent the uncertainty associated with each effect estimate individually and can overlap even when there is a statistically significant difference between the estimates (Cumming & Finch, 2005).”
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“Despite Killeen’s statements to the contrary (p. 350), CIs should be shown around the sample mean, and it is correct that if zero lies outside a CI, the null hypothesis of zero would be rejected, given the data (Cumming & Finch, 2001, 2005).”
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“A comparison of the 99% confidence intervals ( Cummings & Finch, 2005 ) of broad suicidogenic-categories means revealed that physical illness was perceived as responsible for a significantly higher proportion of suicides than were interpersonal problems, which was believed to account for a significantly higher proport…”
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“If there is no overlap, the difference is statistically significant (Cumming and Finch, 2005; Goldstein and Healy, 1995).”
BackgroundWhen I Believe, I Can: Success STEMs from My Perceptions
Kwon, H., Capraro, R. M., & Capraro, M. M. (2021) · Canadian Journal of Science Mathematics and Technology Education · doi:10.1007/s42330-020-00132-4 · Cited by 28
Visualization in Motion: A Research Agenda and Two Evaluations
Yao, L., Bezerianos, A., Vuillemot, R., & Isenberg, P. (2022) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2022.3184993 · Cited by 28
Tell Me Where To Go: Voice-Controlled Hands-Free Locomotion for Virtual Reality Systems
Hombeck, J., Voigt, H., Heggemann, T., Datta, R. R., & Lawonn, K. (2023) · IEEE Conference on Virtual Reality and 3D User Interfaces (VR) · doi:10.1109/vr55154.2023.00028 · Cited by 30
“These results also include the effect size [24].”
BackgroundCohen, J. B., Karpanty, S. M., Fraser, J. D., Watts, B. D., & Truitt, B. R. (2009) · Journal of Wildlife Management · doi:10.2193/2008-042 · Cited by 28
Influence of organizational culture on knowledge transfer: E vidence from the G overnment of D ubai
Rahman, M. H., Moonesar, I. A., Hossain, M. M., & Islam, M. Z. (2018) · Journal of Public Affairs · doi:10.1002/pa.1696 · Cited by 28
“In fact, literature suggests using a 90% instead of 95% confidence level (Batterham & Hopkins, 2006; Cumming & Finch, 2005) and urges not to describe group differences based on its statistical significance (Sterne & Smith, 2001).”
BackgroundCognitive Deliberation, Electoral Decision Making, and Democratic Health*
Barker, D. (2018) · Social Science Quarterly · doi:10.1111/ssqu.12475 · Cited by 3
Brennan, C. J., Roberts, C. A., & Cole, J. C. (2024) · BMJ Open · doi:10.1136/bmjopen-2023-071776 · Cited by 29
“36 For meta-analyses that used prevalence estimates as the outcome, the Freeman-Tukey double arcsine transformation method was applied, which is effective when there are small sample sizes and extreme prevalence estimates.”
MethodMARK, A. F., Korsten, A. C., Guevara, D. U., Dickinson, K. J. M., Maegli, T., Michel, P., Halloy, S. R. P., Lord, J. M., Venn, S., Morgan, J. W., et al. (2015) · Arctic Antarctic and Alpine Research · doi:10.1657/aaar0014-098 · Cited by 27
Comparing interval estimates for small sample ordinal CFA models
Natesan, P. (2015) · Frontiers in Psychology · doi:10.3389/fpsyg.2015.01599 · Cited by 27
Time to Move Again: Does the Bereitschaftspotential Covary with Demands on Internal Timing?
Verleger, R., Haake, M., Baur, A., & Śmigasiewicz, K. (2016) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2016.00642 · Cited by 30
Expressive Faces Confuse Identity
Redfern, A. S., & Benton, C. P. (2017) · i-Perception · doi:10.1177/2041669517731115 · Cited by 27
“This difference is significant – the dotted line indicating veridical performance falls outside the 95% confidence limits for all four conditions (Cumming & Finch, 2005).”
BackgroundConfidence intervals, precision and confounding
Trafimow, D. (2018) · New Ideas in Psychology · doi:10.1016/j.newideapsych.2018.04.005 · Cited by 27
Best Management Practices for Trapping Furbearers in the United States
White, H., Batcheller, G. R., Boggess, E. K., Brown, C. L., Butfiloski, J. W., Decker, T., Erb, J. D., Fall, M. W., Hamilton, D. A., Hiller, T. L., et al. (2020) · Wildlife Monographs · doi:10.1002/wmon.1057 · Cited by 27
“Where applicable, we used informal guidelines (Cumming and Finch 2005) to visually assess differences or patterns in injury scores and trap efficiency across taxonomic groups (we included striped skunks with the mustelids for simplification), broad body‐size class assignments based on average…”
MethodTurner, A. N., Parmar, N., Jovanovski, A., & Hearne, G. (2021) · Strength and conditioning journal · doi:10.1519/ssc.0000000000000613 · Cited by 24
“Confidence intervals are considered an alternate inferential statistic to NHST and were first proposed by Neyman (16) and have since been heavily supported by others (1,5,7,8).”
BackgroundWitt, J. K. (2019) · Meta-Psychology · doi:10.15626/mp.2018.895 · Cited by 29
“There can be cases for which the error bars overlap but the effect is statistically significant at the p .05 level (Cumming & Finch, 2005), but this level of nuance was not presented to the participants.”
BackgroundAnticipated guilt and anti-littering civic engagement in an extended norm activation model
Rosenthal, S., & Yu, M. S. C. (2022) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2022.101757 · Cited by 29
Zammit, S. L., Skouteris, H., Wertheim, E. H., Paxton, S. J., & Milgrom, J. (2008) · Journal of Women s Health · doi:10.1089/jwh.2007.0595 · Cited by 27
Metadata
- Authors
- Cumming, G., & Finch, S.
- Affiliations
- La Trobe University (AU)
- Venue
- American Psychologist
- Published
- 2005
- Volume
- 60
- Issue
- 2
- Pages
- 170-180
- ISSN
- 0003-066X (ISSN-L)
- 1935-990X
- OpenAlex
- W2005534705
- Cited by
- 1,449
- References
- 59
- Citations by year
- 2026: 62 · 2025: 66 · 2024: 74 · 2023: 92 · 2022: 102 · 2021: 110 · 2020: 92 · 2019: 86 · 2018: 80 · 2017: 82 · 2016: 76 · 2015: 89 · 2014: 63 · 2013: 59 · 2012: 48
- FWCI
- 39.36
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Psychologist (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- confidence intervals, error bars, statistical significance testing, interval estimation, scholarly communication
- MeSH terms
- Humans, Confidence Intervals
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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